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Simplifying (4b2 + 5b + -12) + -1(6b2 + -1b + -4) = 0 Reorder the terms: (-12 + 5b + 4b2) + -1(6b2 + -1b + -4) = 0 Remove parenthesis around (-12 + 5b + 4b2) -12 + 5b + 4b2 + -1(6b2 + -1b + -4) = 0 Reorder the terms: -12 + 5b + 4b2 + -1(-4 + -1b + 6b2) = 0 -12 + 5b + 4b2 + (-4 * -1 + -1b * -1 + 6b2 * -1) = 0 -12 + 5b + 4b2 + (4 + 1b + -6b2) = 0 Reorder the terms: -12 + 4 + 5b + 1b + 4b2 + -6b2 = 0 Combine like terms: -12 + 4 = -8 -8 + 5b + 1b + 4b2 + -6b2 = 0 Combine like terms: 5b + 1b = 6b -8 + 6b + 4b2 + -6b2 = 0 Combine like terms: 4b2 + -6b2 = -2b2 -8 + 6b + -2b2 = 0 Solving -8 + 6b + -2b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 3b + -1b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 3b + -1b2)' equal to zero and attempt to solve: Simplifying -4 + 3b + -1b2 = 0 Solving -4 + 3b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -3b + b2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -3b + -4 + b2 = 0 + -4 Reorder the terms: 4 + -4 + -3b + b2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3b + b2 = 0 + -4 -3b + b2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3b + b2 = -4 The b term is -3b. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3b + 2.25 + b2 = -4 + 2.25 Reorder the terms: 2.25 + -3b + b2 = -4 + 2.25 Combine like terms: -4 + 2.25 = -1.75 2.25 + -3b + b2 = -1.75 Factor a perfect square on the left side: (b + -1.5)(b + -1.5) = -1.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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